direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C22.4Q16, C28.28C42, C4⋊C4⋊4C28, (C2×C56)⋊8C4, (C2×C8)⋊4C28, C4.2(C4×C28), (C2×C14).48D8, C28.52(C4⋊C4), (C2×C28).70Q8, C22.7(C7×D8), (C2×C28).507D4, (C22×C8).2C14, (C22×C56).5C2, (C2×C14).19Q16, C14.9(C4.Q8), C23.52(C7×D4), C22.4(C7×Q16), (C2×C14).43SD16, C14.12(C2.D8), C22.9(C7×SD16), (C22×C14).213D4, C14.36(D4⋊C4), C28.103(C22⋊C4), C14.18(Q8⋊C4), (C22×C28).571C22, C14.24(C2.C42), C4.3(C7×C4⋊C4), (C7×C4⋊C4)⋊11C4, (C2×C4⋊C4).2C14, C2.2(C7×C2.D8), C2.2(C7×C4.Q8), (C14×C4⋊C4).29C2, (C2×C4).13(C7×Q8), (C2×C4).40(C2×C28), (C2×C4).112(C7×D4), C2.2(C7×D4⋊C4), C4.19(C7×C22⋊C4), C22.16(C7×C4⋊C4), C2.2(C7×Q8⋊C4), (C2×C14).59(C4⋊C4), (C2×C28).261(C2×C4), C22.29(C7×C22⋊C4), C2.5(C7×C2.C42), (C22×C4).104(C2×C14), (C2×C14).130(C22⋊C4), SmallGroup(448,144)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C22.4Q16
G = < a,b,c,d,e | a7=b2=c2=d8=1, e2=cd4, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd-1 >
Subgroups: 186 in 114 conjugacy classes, 74 normal (30 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C22×C4, C28, C28, C28, C2×C14, C2×C14, C2×C4⋊C4, C22×C8, C56, C2×C28, C2×C28, C2×C28, C22×C14, C22.4Q16, C7×C4⋊C4, C7×C4⋊C4, C2×C56, C2×C56, C22×C28, C22×C28, C14×C4⋊C4, C22×C56, C7×C22.4Q16
Quotients: C1, C2, C4, C22, C7, C2×C4, D4, Q8, C14, C42, C22⋊C4, C4⋊C4, D8, SD16, Q16, C28, C2×C14, C2.C42, D4⋊C4, Q8⋊C4, C4.Q8, C2.D8, C2×C28, C7×D4, C7×Q8, C22.4Q16, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C7×D8, C7×SD16, C7×Q16, C7×C2.C42, C7×D4⋊C4, C7×Q8⋊C4, C7×C4.Q8, C7×C2.D8, C7×C22.4Q16
►Regular action on 448 points
Generators in S448
(1 12 167 159 151 143 135)(2 13 168 160 152 144 136)(3 14 161 153 145 137 129)(4 15 162 154 146 138 130)(5 16 163 155 147 139 131)(6 9 164 156 148 140 132)(7 10 165 157 149 141 133)(8 11 166 158 150 142 134)(17 121 57 49 41 33 25)(18 122 58 50 42 34 26)(19 123 59 51 43 35 27)(20 124 60 52 44 36 28)(21 125 61 53 45 37 29)(22 126 62 54 46 38 30)(23 127 63 55 47 39 31)(24 128 64 56 48 40 32)(65 240 105 97 89 81 73)(66 233 106 98 90 82 74)(67 234 107 99 91 83 75)(68 235 108 100 92 84 76)(69 236 109 101 93 85 77)(70 237 110 102 94 86 78)(71 238 111 103 95 87 79)(72 239 112 104 96 88 80)(113 325 332 309 316 293 300)(114 326 333 310 317 294 301)(115 327 334 311 318 295 302)(116 328 335 312 319 296 303)(117 321 336 305 320 289 304)(118 322 329 306 313 290 297)(119 323 330 307 314 291 298)(120 324 331 308 315 292 299)(169 217 209 201 193 185 177)(170 218 210 202 194 186 178)(171 219 211 203 195 187 179)(172 220 212 204 196 188 180)(173 221 213 205 197 189 181)(174 222 214 206 198 190 182)(175 223 215 207 199 191 183)(176 224 216 208 200 192 184)(225 374 381 363 350 353 339)(226 375 382 364 351 354 340)(227 376 383 365 352 355 341)(228 369 384 366 345 356 342)(229 370 377 367 346 357 343)(230 371 378 368 347 358 344)(231 372 379 361 348 359 337)(232 373 380 362 349 360 338)(241 256 388 273 288 257 272)(242 249 389 274 281 258 265)(243 250 390 275 282 259 266)(244 251 391 276 283 260 267)(245 252 392 277 284 261 268)(246 253 385 278 285 262 269)(247 254 386 279 286 263 270)(248 255 387 280 287 264 271)(393 441 433 425 417 409 401)(394 442 434 426 418 410 402)(395 443 435 427 419 411 403)(396 444 436 428 420 412 404)(397 445 437 429 421 413 405)(398 446 438 430 422 414 406)(399 447 439 431 423 415 407)(400 448 440 432 424 416 408)
(1 21)(2 22)(3 23)(4 24)(5 17)(6 18)(7 19)(8 20)(9 122)(10 123)(11 124)(12 125)(13 126)(14 127)(15 128)(16 121)(25 131)(26 132)(27 133)(28 134)(29 135)(30 136)(31 129)(32 130)(33 139)(34 140)(35 141)(36 142)(37 143)(38 144)(39 137)(40 138)(41 147)(42 148)(43 149)(44 150)(45 151)(46 152)(47 145)(48 146)(49 155)(50 156)(51 157)(52 158)(53 159)(54 160)(55 153)(56 154)(57 163)(58 164)(59 165)(60 166)(61 167)(62 168)(63 161)(64 162)(65 171)(66 172)(67 173)(68 174)(69 175)(70 176)(71 169)(72 170)(73 179)(74 180)(75 181)(76 182)(77 183)(78 184)(79 177)(80 178)(81 187)(82 188)(83 189)(84 190)(85 191)(86 192)(87 185)(88 186)(89 195)(90 196)(91 197)(92 198)(93 199)(94 200)(95 193)(96 194)(97 203)(98 204)(99 205)(100 206)(101 207)(102 208)(103 201)(104 202)(105 211)(106 212)(107 213)(108 214)(109 215)(110 216)(111 209)(112 210)(113 443)(114 444)(115 445)(116 446)(117 447)(118 448)(119 441)(120 442)(217 238)(218 239)(219 240)(220 233)(221 234)(222 235)(223 236)(224 237)(225 255)(226 256)(227 249)(228 250)(229 251)(230 252)(231 253)(232 254)(241 340)(242 341)(243 342)(244 343)(245 344)(246 337)(247 338)(248 339)(257 351)(258 352)(259 345)(260 346)(261 347)(262 348)(263 349)(264 350)(265 355)(266 356)(267 357)(268 358)(269 359)(270 360)(271 353)(272 354)(273 382)(274 383)(275 384)(276 377)(277 378)(278 379)(279 380)(280 381)(281 365)(282 366)(283 367)(284 368)(285 361)(286 362)(287 363)(288 364)(289 407)(290 408)(291 401)(292 402)(293 403)(294 404)(295 405)(296 406)(297 400)(298 393)(299 394)(300 395)(301 396)(302 397)(303 398)(304 399)(305 423)(306 424)(307 417)(308 418)(309 419)(310 420)(311 421)(312 422)(313 416)(314 409)(315 410)(316 411)(317 412)(318 413)(319 414)(320 415)(321 439)(322 440)(323 433)(324 434)(325 435)(326 436)(327 437)(328 438)(329 432)(330 425)(331 426)(332 427)(333 428)(334 429)(335 430)(336 431)(369 390)(370 391)(371 392)(372 385)(373 386)(374 387)(375 388)(376 389)
(1 171)(2 172)(3 173)(4 174)(5 175)(6 176)(7 169)(8 170)(9 224)(10 217)(11 218)(12 219)(13 220)(14 221)(15 222)(16 223)(17 69)(18 70)(19 71)(20 72)(21 65)(22 66)(23 67)(24 68)(25 77)(26 78)(27 79)(28 80)(29 73)(30 74)(31 75)(32 76)(33 85)(34 86)(35 87)(36 88)(37 81)(38 82)(39 83)(40 84)(41 93)(42 94)(43 95)(44 96)(45 89)(46 90)(47 91)(48 92)(49 101)(50 102)(51 103)(52 104)(53 97)(54 98)(55 99)(56 100)(57 109)(58 110)(59 111)(60 112)(61 105)(62 106)(63 107)(64 108)(113 392)(114 385)(115 386)(116 387)(117 388)(118 389)(119 390)(120 391)(121 236)(122 237)(123 238)(124 239)(125 240)(126 233)(127 234)(128 235)(129 181)(130 182)(131 183)(132 184)(133 177)(134 178)(135 179)(136 180)(137 189)(138 190)(139 191)(140 192)(141 185)(142 186)(143 187)(144 188)(145 197)(146 198)(147 199)(148 200)(149 193)(150 194)(151 195)(152 196)(153 205)(154 206)(155 207)(156 208)(157 201)(158 202)(159 203)(160 204)(161 213)(162 214)(163 215)(164 216)(165 209)(166 210)(167 211)(168 212)(225 398)(226 399)(227 400)(228 393)(229 394)(230 395)(231 396)(232 397)(241 289)(242 290)(243 291)(244 292)(245 293)(246 294)(247 295)(248 296)(249 297)(250 298)(251 299)(252 300)(253 301)(254 302)(255 303)(256 304)(257 305)(258 306)(259 307)(260 308)(261 309)(262 310)(263 311)(264 312)(265 313)(266 314)(267 315)(268 316)(269 317)(270 318)(271 319)(272 320)(273 321)(274 322)(275 323)(276 324)(277 325)(278 326)(279 327)(280 328)(281 329)(282 330)(283 331)(284 332)(285 333)(286 334)(287 335)(288 336)(337 404)(338 405)(339 406)(340 407)(341 408)(342 401)(343 402)(344 403)(345 417)(346 418)(347 419)(348 420)(349 421)(350 422)(351 423)(352 424)(353 414)(354 415)(355 416)(356 409)(357 410)(358 411)(359 412)(360 413)(361 428)(362 429)(363 430)(364 431)(365 432)(366 425)(367 426)(368 427)(369 441)(370 442)(371 443)(372 444)(373 445)(374 446)(375 447)(376 448)(377 434)(378 435)(379 436)(380 437)(381 438)(382 439)(383 440)(384 433)
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152)(153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184)(185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248)(249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296)(297 298 299 300 301 302 303 304)(305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320)(321 322 323 324 325 326 327 328)(329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344)(345 346 347 348 349 350 351 352)(353 354 355 356 357 358 359 360)(361 362 363 364 365 366 367 368)(369 370 371 372 373 374 375 376)(377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392)(393 394 395 396 397 398 399 400)(401 402 403 404 405 406 407 408)(409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424)(425 426 427 428 429 430 431 432)(433 434 435 436 437 438 439 440)(441 442 443 444 445 446 447 448)
(1 298 175 254)(2 400 176 231)(3 304 169 252)(4 398 170 229)(5 302 171 250)(6 396 172 227)(7 300 173 256)(8 394 174 225)(9 444 220 376)(10 113 221 388)(11 442 222 374)(12 119 223 386)(13 448 224 372)(14 117 217 392)(15 446 218 370)(16 115 219 390)(17 397 65 228)(18 301 66 249)(19 395 67 226)(20 299 68 255)(21 393 69 232)(22 297 70 253)(23 399 71 230)(24 303 72 251)(25 405 73 342)(26 294 74 242)(27 403 75 340)(28 292 76 248)(29 401 77 338)(30 290 78 246)(31 407 79 344)(32 296 80 244)(33 413 81 356)(34 317 82 265)(35 411 83 354)(36 315 84 271)(37 409 85 360)(38 313 86 269)(39 415 87 358)(40 319 88 267)(41 421 89 345)(42 310 90 258)(43 419 91 351)(44 308 92 264)(45 417 93 349)(46 306 94 262)(47 423 95 347)(48 312 96 260)(49 429 97 366)(50 333 98 281)(51 427 99 364)(52 331 100 287)(53 425 101 362)(54 329 102 285)(55 431 103 368)(56 335 104 283)(57 437 105 384)(58 326 106 274)(59 435 107 382)(60 324 108 280)(61 433 109 380)(62 322 110 278)(63 439 111 378)(64 328 112 276)(114 233 389 122)(116 239 391 128)(118 237 385 126)(120 235 387 124)(121 445 240 369)(123 443 234 375)(125 441 236 373)(127 447 238 371)(129 289 177 245)(130 406 178 343)(131 295 179 243)(132 404 180 341)(133 293 181 241)(134 402 182 339)(135 291 183 247)(136 408 184 337)(137 320 185 268)(138 414 186 357)(139 318 187 266)(140 412 188 355)(141 316 189 272)(142 410 190 353)(143 314 191 270)(144 416 192 359)(145 305 193 261)(146 422 194 346)(147 311 195 259)(148 420 196 352)(149 309 197 257)(150 418 198 350)(151 307 199 263)(152 424 200 348)(153 336 201 284)(154 430 202 367)(155 334 203 282)(156 428 204 365)(157 332 205 288)(158 426 206 363)(159 330 207 286)(160 432 208 361)(161 321 209 277)(162 438 210 377)(163 327 211 275)(164 436 212 383)(165 325 213 273)(166 434 214 381)(167 323 215 279)(168 440 216 379)
G:=sub<Sym(448)| (1,12,167,159,151,143,135)(2,13,168,160,152,144,136)(3,14,161,153,145,137,129)(4,15,162,154,146,138,130)(5,16,163,155,147,139,131)(6,9,164,156,148,140,132)(7,10,165,157,149,141,133)(8,11,166,158,150,142,134)(17,121,57,49,41,33,25)(18,122,58,50,42,34,26)(19,123,59,51,43,35,27)(20,124,60,52,44,36,28)(21,125,61,53,45,37,29)(22,126,62,54,46,38,30)(23,127,63,55,47,39,31)(24,128,64,56,48,40,32)(65,240,105,97,89,81,73)(66,233,106,98,90,82,74)(67,234,107,99,91,83,75)(68,235,108,100,92,84,76)(69,236,109,101,93,85,77)(70,237,110,102,94,86,78)(71,238,111,103,95,87,79)(72,239,112,104,96,88,80)(113,325,332,309,316,293,300)(114,326,333,310,317,294,301)(115,327,334,311,318,295,302)(116,328,335,312,319,296,303)(117,321,336,305,320,289,304)(118,322,329,306,313,290,297)(119,323,330,307,314,291,298)(120,324,331,308,315,292,299)(169,217,209,201,193,185,177)(170,218,210,202,194,186,178)(171,219,211,203,195,187,179)(172,220,212,204,196,188,180)(173,221,213,205,197,189,181)(174,222,214,206,198,190,182)(175,223,215,207,199,191,183)(176,224,216,208,200,192,184)(225,374,381,363,350,353,339)(226,375,382,364,351,354,340)(227,376,383,365,352,355,341)(228,369,384,366,345,356,342)(229,370,377,367,346,357,343)(230,371,378,368,347,358,344)(231,372,379,361,348,359,337)(232,373,380,362,349,360,338)(241,256,388,273,288,257,272)(242,249,389,274,281,258,265)(243,250,390,275,282,259,266)(244,251,391,276,283,260,267)(245,252,392,277,284,261,268)(246,253,385,278,285,262,269)(247,254,386,279,286,263,270)(248,255,387,280,287,264,271)(393,441,433,425,417,409,401)(394,442,434,426,418,410,402)(395,443,435,427,419,411,403)(396,444,436,428,420,412,404)(397,445,437,429,421,413,405)(398,446,438,430,422,414,406)(399,447,439,431,423,415,407)(400,448,440,432,424,416,408), (1,21)(2,22)(3,23)(4,24)(5,17)(6,18)(7,19)(8,20)(9,122)(10,123)(11,124)(12,125)(13,126)(14,127)(15,128)(16,121)(25,131)(26,132)(27,133)(28,134)(29,135)(30,136)(31,129)(32,130)(33,139)(34,140)(35,141)(36,142)(37,143)(38,144)(39,137)(40,138)(41,147)(42,148)(43,149)(44,150)(45,151)(46,152)(47,145)(48,146)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,153)(56,154)(57,163)(58,164)(59,165)(60,166)(61,167)(62,168)(63,161)(64,162)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,169)(72,170)(73,179)(74,180)(75,181)(76,182)(77,183)(78,184)(79,177)(80,178)(81,187)(82,188)(83,189)(84,190)(85,191)(86,192)(87,185)(88,186)(89,195)(90,196)(91,197)(92,198)(93,199)(94,200)(95,193)(96,194)(97,203)(98,204)(99,205)(100,206)(101,207)(102,208)(103,201)(104,202)(105,211)(106,212)(107,213)(108,214)(109,215)(110,216)(111,209)(112,210)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,441)(120,442)(217,238)(218,239)(219,240)(220,233)(221,234)(222,235)(223,236)(224,237)(225,255)(226,256)(227,249)(228,250)(229,251)(230,252)(231,253)(232,254)(241,340)(242,341)(243,342)(244,343)(245,344)(246,337)(247,338)(248,339)(257,351)(258,352)(259,345)(260,346)(261,347)(262,348)(263,349)(264,350)(265,355)(266,356)(267,357)(268,358)(269,359)(270,360)(271,353)(272,354)(273,382)(274,383)(275,384)(276,377)(277,378)(278,379)(279,380)(280,381)(281,365)(282,366)(283,367)(284,368)(285,361)(286,362)(287,363)(288,364)(289,407)(290,408)(291,401)(292,402)(293,403)(294,404)(295,405)(296,406)(297,400)(298,393)(299,394)(300,395)(301,396)(302,397)(303,398)(304,399)(305,423)(306,424)(307,417)(308,418)(309,419)(310,420)(311,421)(312,422)(313,416)(314,409)(315,410)(316,411)(317,412)(318,413)(319,414)(320,415)(321,439)(322,440)(323,433)(324,434)(325,435)(326,436)(327,437)(328,438)(329,432)(330,425)(331,426)(332,427)(333,428)(334,429)(335,430)(336,431)(369,390)(370,391)(371,392)(372,385)(373,386)(374,387)(375,388)(376,389), (1,171)(2,172)(3,173)(4,174)(5,175)(6,176)(7,169)(8,170)(9,224)(10,217)(11,218)(12,219)(13,220)(14,221)(15,222)(16,223)(17,69)(18,70)(19,71)(20,72)(21,65)(22,66)(23,67)(24,68)(25,77)(26,78)(27,79)(28,80)(29,73)(30,74)(31,75)(32,76)(33,85)(34,86)(35,87)(36,88)(37,81)(38,82)(39,83)(40,84)(41,93)(42,94)(43,95)(44,96)(45,89)(46,90)(47,91)(48,92)(49,101)(50,102)(51,103)(52,104)(53,97)(54,98)(55,99)(56,100)(57,109)(58,110)(59,111)(60,112)(61,105)(62,106)(63,107)(64,108)(113,392)(114,385)(115,386)(116,387)(117,388)(118,389)(119,390)(120,391)(121,236)(122,237)(123,238)(124,239)(125,240)(126,233)(127,234)(128,235)(129,181)(130,182)(131,183)(132,184)(133,177)(134,178)(135,179)(136,180)(137,189)(138,190)(139,191)(140,192)(141,185)(142,186)(143,187)(144,188)(145,197)(146,198)(147,199)(148,200)(149,193)(150,194)(151,195)(152,196)(153,205)(154,206)(155,207)(156,208)(157,201)(158,202)(159,203)(160,204)(161,213)(162,214)(163,215)(164,216)(165,209)(166,210)(167,211)(168,212)(225,398)(226,399)(227,400)(228,393)(229,394)(230,395)(231,396)(232,397)(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)(248,296)(249,297)(250,298)(251,299)(252,300)(253,301)(254,302)(255,303)(256,304)(257,305)(258,306)(259,307)(260,308)(261,309)(262,310)(263,311)(264,312)(265,313)(266,314)(267,315)(268,316)(269,317)(270,318)(271,319)(272,320)(273,321)(274,322)(275,323)(276,324)(277,325)(278,326)(279,327)(280,328)(281,329)(282,330)(283,331)(284,332)(285,333)(286,334)(287,335)(288,336)(337,404)(338,405)(339,406)(340,407)(341,408)(342,401)(343,402)(344,403)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)(353,414)(354,415)(355,416)(356,409)(357,410)(358,411)(359,412)(360,413)(361,428)(362,429)(363,430)(364,431)(365,432)(366,425)(367,426)(368,427)(369,441)(370,442)(371,443)(372,444)(373,445)(374,446)(375,447)(376,448)(377,434)(378,435)(379,436)(380,437)(381,438)(382,439)(383,440)(384,433), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296)(297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328)(329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344)(345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376)(377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424)(425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440)(441,442,443,444,445,446,447,448), (1,298,175,254)(2,400,176,231)(3,304,169,252)(4,398,170,229)(5,302,171,250)(6,396,172,227)(7,300,173,256)(8,394,174,225)(9,444,220,376)(10,113,221,388)(11,442,222,374)(12,119,223,386)(13,448,224,372)(14,117,217,392)(15,446,218,370)(16,115,219,390)(17,397,65,228)(18,301,66,249)(19,395,67,226)(20,299,68,255)(21,393,69,232)(22,297,70,253)(23,399,71,230)(24,303,72,251)(25,405,73,342)(26,294,74,242)(27,403,75,340)(28,292,76,248)(29,401,77,338)(30,290,78,246)(31,407,79,344)(32,296,80,244)(33,413,81,356)(34,317,82,265)(35,411,83,354)(36,315,84,271)(37,409,85,360)(38,313,86,269)(39,415,87,358)(40,319,88,267)(41,421,89,345)(42,310,90,258)(43,419,91,351)(44,308,92,264)(45,417,93,349)(46,306,94,262)(47,423,95,347)(48,312,96,260)(49,429,97,366)(50,333,98,281)(51,427,99,364)(52,331,100,287)(53,425,101,362)(54,329,102,285)(55,431,103,368)(56,335,104,283)(57,437,105,384)(58,326,106,274)(59,435,107,382)(60,324,108,280)(61,433,109,380)(62,322,110,278)(63,439,111,378)(64,328,112,276)(114,233,389,122)(116,239,391,128)(118,237,385,126)(120,235,387,124)(121,445,240,369)(123,443,234,375)(125,441,236,373)(127,447,238,371)(129,289,177,245)(130,406,178,343)(131,295,179,243)(132,404,180,341)(133,293,181,241)(134,402,182,339)(135,291,183,247)(136,408,184,337)(137,320,185,268)(138,414,186,357)(139,318,187,266)(140,412,188,355)(141,316,189,272)(142,410,190,353)(143,314,191,270)(144,416,192,359)(145,305,193,261)(146,422,194,346)(147,311,195,259)(148,420,196,352)(149,309,197,257)(150,418,198,350)(151,307,199,263)(152,424,200,348)(153,336,201,284)(154,430,202,367)(155,334,203,282)(156,428,204,365)(157,332,205,288)(158,426,206,363)(159,330,207,286)(160,432,208,361)(161,321,209,277)(162,438,210,377)(163,327,211,275)(164,436,212,383)(165,325,213,273)(166,434,214,381)(167,323,215,279)(168,440,216,379)>;
G:=Group( (1,12,167,159,151,143,135)(2,13,168,160,152,144,136)(3,14,161,153,145,137,129)(4,15,162,154,146,138,130)(5,16,163,155,147,139,131)(6,9,164,156,148,140,132)(7,10,165,157,149,141,133)(8,11,166,158,150,142,134)(17,121,57,49,41,33,25)(18,122,58,50,42,34,26)(19,123,59,51,43,35,27)(20,124,60,52,44,36,28)(21,125,61,53,45,37,29)(22,126,62,54,46,38,30)(23,127,63,55,47,39,31)(24,128,64,56,48,40,32)(65,240,105,97,89,81,73)(66,233,106,98,90,82,74)(67,234,107,99,91,83,75)(68,235,108,100,92,84,76)(69,236,109,101,93,85,77)(70,237,110,102,94,86,78)(71,238,111,103,95,87,79)(72,239,112,104,96,88,80)(113,325,332,309,316,293,300)(114,326,333,310,317,294,301)(115,327,334,311,318,295,302)(116,328,335,312,319,296,303)(117,321,336,305,320,289,304)(118,322,329,306,313,290,297)(119,323,330,307,314,291,298)(120,324,331,308,315,292,299)(169,217,209,201,193,185,177)(170,218,210,202,194,186,178)(171,219,211,203,195,187,179)(172,220,212,204,196,188,180)(173,221,213,205,197,189,181)(174,222,214,206,198,190,182)(175,223,215,207,199,191,183)(176,224,216,208,200,192,184)(225,374,381,363,350,353,339)(226,375,382,364,351,354,340)(227,376,383,365,352,355,341)(228,369,384,366,345,356,342)(229,370,377,367,346,357,343)(230,371,378,368,347,358,344)(231,372,379,361,348,359,337)(232,373,380,362,349,360,338)(241,256,388,273,288,257,272)(242,249,389,274,281,258,265)(243,250,390,275,282,259,266)(244,251,391,276,283,260,267)(245,252,392,277,284,261,268)(246,253,385,278,285,262,269)(247,254,386,279,286,263,270)(248,255,387,280,287,264,271)(393,441,433,425,417,409,401)(394,442,434,426,418,410,402)(395,443,435,427,419,411,403)(396,444,436,428,420,412,404)(397,445,437,429,421,413,405)(398,446,438,430,422,414,406)(399,447,439,431,423,415,407)(400,448,440,432,424,416,408), (1,21)(2,22)(3,23)(4,24)(5,17)(6,18)(7,19)(8,20)(9,122)(10,123)(11,124)(12,125)(13,126)(14,127)(15,128)(16,121)(25,131)(26,132)(27,133)(28,134)(29,135)(30,136)(31,129)(32,130)(33,139)(34,140)(35,141)(36,142)(37,143)(38,144)(39,137)(40,138)(41,147)(42,148)(43,149)(44,150)(45,151)(46,152)(47,145)(48,146)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,153)(56,154)(57,163)(58,164)(59,165)(60,166)(61,167)(62,168)(63,161)(64,162)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,169)(72,170)(73,179)(74,180)(75,181)(76,182)(77,183)(78,184)(79,177)(80,178)(81,187)(82,188)(83,189)(84,190)(85,191)(86,192)(87,185)(88,186)(89,195)(90,196)(91,197)(92,198)(93,199)(94,200)(95,193)(96,194)(97,203)(98,204)(99,205)(100,206)(101,207)(102,208)(103,201)(104,202)(105,211)(106,212)(107,213)(108,214)(109,215)(110,216)(111,209)(112,210)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,441)(120,442)(217,238)(218,239)(219,240)(220,233)(221,234)(222,235)(223,236)(224,237)(225,255)(226,256)(227,249)(228,250)(229,251)(230,252)(231,253)(232,254)(241,340)(242,341)(243,342)(244,343)(245,344)(246,337)(247,338)(248,339)(257,351)(258,352)(259,345)(260,346)(261,347)(262,348)(263,349)(264,350)(265,355)(266,356)(267,357)(268,358)(269,359)(270,360)(271,353)(272,354)(273,382)(274,383)(275,384)(276,377)(277,378)(278,379)(279,380)(280,381)(281,365)(282,366)(283,367)(284,368)(285,361)(286,362)(287,363)(288,364)(289,407)(290,408)(291,401)(292,402)(293,403)(294,404)(295,405)(296,406)(297,400)(298,393)(299,394)(300,395)(301,396)(302,397)(303,398)(304,399)(305,423)(306,424)(307,417)(308,418)(309,419)(310,420)(311,421)(312,422)(313,416)(314,409)(315,410)(316,411)(317,412)(318,413)(319,414)(320,415)(321,439)(322,440)(323,433)(324,434)(325,435)(326,436)(327,437)(328,438)(329,432)(330,425)(331,426)(332,427)(333,428)(334,429)(335,430)(336,431)(369,390)(370,391)(371,392)(372,385)(373,386)(374,387)(375,388)(376,389), 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(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296)(297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328)(329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344)(345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376)(377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424)(425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440)(441,442,443,444,445,446,447,448), (1,298,175,254)(2,400,176,231)(3,304,169,252)(4,398,170,229)(5,302,171,250)(6,396,172,227)(7,300,173,256)(8,394,174,225)(9,444,220,376)(10,113,221,388)(11,442,222,374)(12,119,223,386)(13,448,224,372)(14,117,217,392)(15,446,218,370)(16,115,219,390)(17,397,65,228)(18,301,66,249)(19,395,67,226)(20,299,68,255)(21,393,69,232)(22,297,70,253)(23,399,71,230)(24,303,72,251)(25,405,73,342)(26,294,74,242)(27,403,75,340)(28,292,76,248)(29,401,77,338)(30,290,78,246)(31,407,79,344)(32,296,80,244)(33,413,81,356)(34,317,82,265)(35,411,83,354)(36,315,84,271)(37,409,85,360)(38,313,86,269)(39,415,87,358)(40,319,88,267)(41,421,89,345)(42,310,90,258)(43,419,91,351)(44,308,92,264)(45,417,93,349)(46,306,94,262)(47,423,95,347)(48,312,96,260)(49,429,97,366)(50,333,98,281)(51,427,99,364)(52,331,100,287)(53,425,101,362)(54,329,102,285)(55,431,103,368)(56,335,104,283)(57,437,105,384)(58,326,106,274)(59,435,107,382)(60,324,108,280)(61,433,109,380)(62,322,110,278)(63,439,111,378)(64,328,112,276)(114,233,389,122)(116,239,391,128)(118,237,385,126)(120,235,387,124)(121,445,240,369)(123,443,234,375)(125,441,236,373)(127,447,238,371)(129,289,177,245)(130,406,178,343)(131,295,179,243)(132,404,180,341)(133,293,181,241)(134,402,182,339)(135,291,183,247)(136,408,184,337)(137,320,185,268)(138,414,186,357)(139,318,187,266)(140,412,188,355)(141,316,189,272)(142,410,190,353)(143,314,191,270)(144,416,192,359)(145,305,193,261)(146,422,194,346)(147,311,195,259)(148,420,196,352)(149,309,197,257)(150,418,198,350)(151,307,199,263)(152,424,200,348)(153,336,201,284)(154,430,202,367)(155,334,203,282)(156,428,204,365)(157,332,205,288)(158,426,206,363)(159,330,207,286)(160,432,208,361)(161,321,209,277)(162,438,210,377)(163,327,211,275)(164,436,212,383)(165,325,213,273)(166,434,214,381)(167,323,215,279)(168,440,216,379) );
G=PermutationGroup([[(1,12,167,159,151,143,135),(2,13,168,160,152,144,136),(3,14,161,153,145,137,129),(4,15,162,154,146,138,130),(5,16,163,155,147,139,131),(6,9,164,156,148,140,132),(7,10,165,157,149,141,133),(8,11,166,158,150,142,134),(17,121,57,49,41,33,25),(18,122,58,50,42,34,26),(19,123,59,51,43,35,27),(20,124,60,52,44,36,28),(21,125,61,53,45,37,29),(22,126,62,54,46,38,30),(23,127,63,55,47,39,31),(24,128,64,56,48,40,32),(65,240,105,97,89,81,73),(66,233,106,98,90,82,74),(67,234,107,99,91,83,75),(68,235,108,100,92,84,76),(69,236,109,101,93,85,77),(70,237,110,102,94,86,78),(71,238,111,103,95,87,79),(72,239,112,104,96,88,80),(113,325,332,309,316,293,300),(114,326,333,310,317,294,301),(115,327,334,311,318,295,302),(116,328,335,312,319,296,303),(117,321,336,305,320,289,304),(118,322,329,306,313,290,297),(119,323,330,307,314,291,298),(120,324,331,308,315,292,299),(169,217,209,201,193,185,177),(170,218,210,202,194,186,178),(171,219,211,203,195,187,179),(172,220,212,204,196,188,180),(173,221,213,205,197,189,181),(174,222,214,206,198,190,182),(175,223,215,207,199,191,183),(176,224,216,208,200,192,184),(225,374,381,363,350,353,339),(226,375,382,364,351,354,340),(227,376,383,365,352,355,341),(228,369,384,366,345,356,342),(229,370,377,367,346,357,343),(230,371,378,368,347,358,344),(231,372,379,361,348,359,337),(232,373,380,362,349,360,338),(241,256,388,273,288,257,272),(242,249,389,274,281,258,265),(243,250,390,275,282,259,266),(244,251,391,276,283,260,267),(245,252,392,277,284,261,268),(246,253,385,278,285,262,269),(247,254,386,279,286,263,270),(248,255,387,280,287,264,271),(393,441,433,425,417,409,401),(394,442,434,426,418,410,402),(395,443,435,427,419,411,403),(396,444,436,428,420,412,404),(397,445,437,429,421,413,405),(398,446,438,430,422,414,406),(399,447,439,431,423,415,407),(400,448,440,432,424,416,408)], [(1,21),(2,22),(3,23),(4,24),(5,17),(6,18),(7,19),(8,20),(9,122),(10,123),(11,124),(12,125),(13,126),(14,127),(15,128),(16,121),(25,131),(26,132),(27,133),(28,134),(29,135),(30,136),(31,129),(32,130),(33,139),(34,140),(35,141),(36,142),(37,143),(38,144),(39,137),(40,138),(41,147),(42,148),(43,149),(44,150),(45,151),(46,152),(47,145),(48,146),(49,155),(50,156),(51,157),(52,158),(53,159),(54,160),(55,153),(56,154),(57,163),(58,164),(59,165),(60,166),(61,167),(62,168),(63,161),(64,162),(65,171),(66,172),(67,173),(68,174),(69,175),(70,176),(71,169),(72,170),(73,179),(74,180),(75,181),(76,182),(77,183),(78,184),(79,177),(80,178),(81,187),(82,188),(83,189),(84,190),(85,191),(86,192),(87,185),(88,186),(89,195),(90,196),(91,197),(92,198),(93,199),(94,200),(95,193),(96,194),(97,203),(98,204),(99,205),(100,206),(101,207),(102,208),(103,201),(104,202),(105,211),(106,212),(107,213),(108,214),(109,215),(110,216),(111,209),(112,210),(113,443),(114,444),(115,445),(116,446),(117,447),(118,448),(119,441),(120,442),(217,238),(218,239),(219,240),(220,233),(221,234),(222,235),(223,236),(224,237),(225,255),(226,256),(227,249),(228,250),(229,251),(230,252),(231,253),(232,254),(241,340),(242,341),(243,342),(244,343),(245,344),(246,337),(247,338),(248,339),(257,351),(258,352),(259,345),(260,346),(261,347),(262,348),(263,349),(264,350),(265,355),(266,356),(267,357),(268,358),(269,359),(270,360),(271,353),(272,354),(273,382),(274,383),(275,384),(276,377),(277,378),(278,379),(279,380),(280,381),(281,365),(282,366),(283,367),(284,368),(285,361),(286,362),(287,363),(288,364),(289,407),(290,408),(291,401),(292,402),(293,403),(294,404),(295,405),(296,406),(297,400),(298,393),(299,394),(300,395),(301,396),(302,397),(303,398),(304,399),(305,423),(306,424),(307,417),(308,418),(309,419),(310,420),(311,421),(312,422),(313,416),(314,409),(315,410),(316,411),(317,412),(318,413),(319,414),(320,415),(321,439),(322,440),(323,433),(324,434),(325,435),(326,436),(327,437),(328,438),(329,432),(330,425),(331,426),(332,427),(333,428),(334,429),(335,430),(336,431),(369,390),(370,391),(371,392),(372,385),(373,386),(374,387),(375,388),(376,389)], [(1,171),(2,172),(3,173),(4,174),(5,175),(6,176),(7,169),(8,170),(9,224),(10,217),(11,218),(12,219),(13,220),(14,221),(15,222),(16,223),(17,69),(18,70),(19,71),(20,72),(21,65),(22,66),(23,67),(24,68),(25,77),(26,78),(27,79),(28,80),(29,73),(30,74),(31,75),(32,76),(33,85),(34,86),(35,87),(36,88),(37,81),(38,82),(39,83),(40,84),(41,93),(42,94),(43,95),(44,96),(45,89),(46,90),(47,91),(48,92),(49,101),(50,102),(51,103),(52,104),(53,97),(54,98),(55,99),(56,100),(57,109),(58,110),(59,111),(60,112),(61,105),(62,106),(63,107),(64,108),(113,392),(114,385),(115,386),(116,387),(117,388),(118,389),(119,390),(120,391),(121,236),(122,237),(123,238),(124,239),(125,240),(126,233),(127,234),(128,235),(129,181),(130,182),(131,183),(132,184),(133,177),(134,178),(135,179),(136,180),(137,189),(138,190),(139,191),(140,192),(141,185),(142,186),(143,187),(144,188),(145,197),(146,198),(147,199),(148,200),(149,193),(150,194),(151,195),(152,196),(153,205),(154,206),(155,207),(156,208),(157,201),(158,202),(159,203),(160,204),(161,213),(162,214),(163,215),(164,216),(165,209),(166,210),(167,211),(168,212),(225,398),(226,399),(227,400),(228,393),(229,394),(230,395),(231,396),(232,397),(241,289),(242,290),(243,291),(244,292),(245,293),(246,294),(247,295),(248,296),(249,297),(250,298),(251,299),(252,300),(253,301),(254,302),(255,303),(256,304),(257,305),(258,306),(259,307),(260,308),(261,309),(262,310),(263,311),(264,312),(265,313),(266,314),(267,315),(268,316),(269,317),(270,318),(271,319),(272,320),(273,321),(274,322),(275,323),(276,324),(277,325),(278,326),(279,327),(280,328),(281,329),(282,330),(283,331),(284,332),(285,333),(286,334),(287,335),(288,336),(337,404),(338,405),(339,406),(340,407),(341,408),(342,401),(343,402),(344,403),(345,417),(346,418),(347,419),(348,420),(349,421),(350,422),(351,423),(352,424),(353,414),(354,415),(355,416),(356,409),(357,410),(358,411),(359,412),(360,413),(361,428),(362,429),(363,430),(364,431),(365,432),(366,425),(367,426),(368,427),(369,441),(370,442),(371,443),(372,444),(373,445),(374,446),(375,447),(376,448),(377,434),(378,435),(379,436),(380,437),(381,438),(382,439),(383,440),(384,433)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32),(33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64),(65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128),(129,130,131,132,133,134,135,136),(137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152),(153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176),(177,178,179,180,181,182,183,184),(185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224),(225,226,227,228,229,230,231,232),(233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248),(249,250,251,252,253,254,255,256),(257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272),(273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288),(289,290,291,292,293,294,295,296),(297,298,299,300,301,302,303,304),(305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320),(321,322,323,324,325,326,327,328),(329,330,331,332,333,334,335,336),(337,338,339,340,341,342,343,344),(345,346,347,348,349,350,351,352),(353,354,355,356,357,358,359,360),(361,362,363,364,365,366,367,368),(369,370,371,372,373,374,375,376),(377,378,379,380,381,382,383,384),(385,386,387,388,389,390,391,392),(393,394,395,396,397,398,399,400),(401,402,403,404,405,406,407,408),(409,410,411,412,413,414,415,416),(417,418,419,420,421,422,423,424),(425,426,427,428,429,430,431,432),(433,434,435,436,437,438,439,440),(441,442,443,444,445,446,447,448)], [(1,298,175,254),(2,400,176,231),(3,304,169,252),(4,398,170,229),(5,302,171,250),(6,396,172,227),(7,300,173,256),(8,394,174,225),(9,444,220,376),(10,113,221,388),(11,442,222,374),(12,119,223,386),(13,448,224,372),(14,117,217,392),(15,446,218,370),(16,115,219,390),(17,397,65,228),(18,301,66,249),(19,395,67,226),(20,299,68,255),(21,393,69,232),(22,297,70,253),(23,399,71,230),(24,303,72,251),(25,405,73,342),(26,294,74,242),(27,403,75,340),(28,292,76,248),(29,401,77,338),(30,290,78,246),(31,407,79,344),(32,296,80,244),(33,413,81,356),(34,317,82,265),(35,411,83,354),(36,315,84,271),(37,409,85,360),(38,313,86,269),(39,415,87,358),(40,319,88,267),(41,421,89,345),(42,310,90,258),(43,419,91,351),(44,308,92,264),(45,417,93,349),(46,306,94,262),(47,423,95,347),(48,312,96,260),(49,429,97,366),(50,333,98,281),(51,427,99,364),(52,331,100,287),(53,425,101,362),(54,329,102,285),(55,431,103,368),(56,335,104,283),(57,437,105,384),(58,326,106,274),(59,435,107,382),(60,324,108,280),(61,433,109,380),(62,322,110,278),(63,439,111,378),(64,328,112,276),(114,233,389,122),(116,239,391,128),(118,237,385,126),(120,235,387,124),(121,445,240,369),(123,443,234,375),(125,441,236,373),(127,447,238,371),(129,289,177,245),(130,406,178,343),(131,295,179,243),(132,404,180,341),(133,293,181,241),(134,402,182,339),(135,291,183,247),(136,408,184,337),(137,320,185,268),(138,414,186,357),(139,318,187,266),(140,412,188,355),(141,316,189,272),(142,410,190,353),(143,314,191,270),(144,416,192,359),(145,305,193,261),(146,422,194,346),(147,311,195,259),(148,420,196,352),(149,309,197,257),(150,418,198,350),(151,307,199,263),(152,424,200,348),(153,336,201,284),(154,430,202,367),(155,334,203,282),(156,428,204,365),(157,332,205,288),(158,426,206,363),(159,330,207,286),(160,432,208,361),(161,321,209,277),(162,438,210,377),(163,327,211,275),(164,436,212,383),(165,325,213,273),(166,434,214,381),(167,323,215,279),(168,440,216,379)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14AP | 28A | ··· | 28X | 28Y | ··· | 28BT | 56A | ··· | 56AV |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C7 | C14 | C14 | C28 | C28 | D4 | Q8 | D4 | D8 | SD16 | Q16 | C7×D4 | C7×Q8 | C7×D4 | C7×D8 | C7×SD16 | C7×Q16 |
| kernel | C7×C22.4Q16 | C14×C4⋊C4 | C22×C56 | C7×C4⋊C4 | C2×C56 | C22.4Q16 | C2×C4⋊C4 | C22×C8 | C4⋊C4 | C2×C8 | C2×C28 | C2×C28 | C22×C14 | C2×C14 | C2×C14 | C2×C14 | C2×C4 | C2×C4 | C23 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 8 | 4 | 6 | 12 | 6 | 48 | 24 | 2 | 1 | 1 | 2 | 4 | 2 | 12 | 6 | 6 | 12 | 24 | 12 |
Matrix representation of C7×C22.4Q16 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 30 | 0 |
| 0 | 0 | 0 | 30 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 98 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 51 | 62 |
| 0 | 0 | 82 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 110 | 24 |
| 0 | 0 | 9 | 3 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,30,0,0,0,0,30],[112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[98,0,0,0,0,15,0,0,0,0,51,82,0,0,62,0],[1,0,0,0,0,98,0,0,0,0,110,9,0,0,24,3] >;
C7×C22.4Q16 in GAP, Magma, Sage, TeX
C_7\times C_2^2._4Q_{16} % in TeX
G:=Group("C7xC2^2.4Q16"); // GroupNames label
G:=SmallGroup(448,144);
// by ID
G=gap.SmallGroup(448,144);
# by ID
G:=PCGroup([7,-2,-2,-7,-2,-2,-2,-2,392,421,792,7059,248,14117,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^7=b^2=c^2=d^8=1,e^2=c*d^4,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b*d^-1>;
// generators/relations